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Chapter 1: Problem 70

Perform each indicated operation. $$ (3-7)+4 $$

Short Answer

Expert verified
The result is 0.

Step by step solution

01

Identify the Operations

First, recognize that there are two operations in this expression: subtraction and addition.
02

Perform the Subtraction

Subtract 7 from 3: \(3 - 7 = -4\)
03

Perform the Addition

Add 4 to the result from the previous step: \(-4 + 4 = 0\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtraction
Subtraction is taking one quantity away from another. In the exercise, we subtract 7 from 3. When performing subtraction with negative results, remember that subtracting a larger number from a smaller one yields a negative result. For instance, in our problem:
  • 3 - 7
This translates to starting at 3 on a number line and moving 7 steps to the left, which lands us at -4. Subtraction can be visualized with number lines, which help us to understand movements and positions in relation to zero.
Addition
Addition is the process of bringing two or more numbers together to make a new total. After performing the subtraction in our problem, we are left with -4. The next step is to add 4 to -4. Remember, adding a positive number to a negative number means moving to the right on the number line.
  • -4 + 4
With -4 on the number line, adding 4 shifts us four places to the right, bringing us back to 0. Addition helps us combine amounts and understand aggregation, especially crucial when dealing with positive and negative numbers.
Order of Operations
The order of operations is a set of rules to determine the sequence in which we perform mathematical operations. Commonly remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)), it ensures consistency and correctness in our calculations. In the given exercise:
  • (3 - 7) + 4
We first deal with the subtraction inside the parentheses. This highlights the importance of following the right order: do the subtraction first ( 3 - 7 = -4), then the addition (-4 + 4 = 0). Following these steps ensures you reach the correct result.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(-15,29,8,-6\)

Find each difference. $$ \frac{1}{3}-\left(-\frac{4}{3}\right) $$

Decide whether each statement is true or false. \(|13-8| \leq|7-4|\)

Find each difference. $$ -6-(-2) $$

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of 12 and the difference between 9 and \(-8\)
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